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(CNN)Trailing Hillary Clinton among Democrats, Bernie Sanders could be looking across the aisle for new support -- specifically at down-on-their-luck voters drawn to Donald Trump's populist economic message.

In a taped interview with CBS' "Face the Nation" on Sunday, the Vermont senator -- a self-proclaimed democratic-socialist -- made an overture to "angry" Americans frustrated by financial woes and concerned by foreign terrorism.

"What I'm suggesting is that what Trump has done with some success has taken that anger, taken those fears -- which are legitimate -- and converted them into anger against Mexicans, anger against Muslims," Sanders said.

But while he made the case that both candidates had tapped into a similar frustration, Sanders was careful to underline the different approach he offered -- a sharp contrast to Trump's often controversial or demeaning rhetorical spasms.

"For his working class and middle class support," Sanders said, "we can make the case that if we really want to address the issues that people are concerned about...we need policies that bring us together, that take on the greed of Wall Street the greed of corporate America and create a middle class that works for all of us rather than an economy that works just for a few."

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Sanders' comments obviously caught Trump's attention. Hours later, he responded, but only to Sanders' suggestion that his economic plan would hurt low-wage workers.

"@BernieSanders-who blew his campaign when he gave Hillary a pass on her e-mail crime, said that I feel wages in America are too high. Lie!," Trump tweeted a little before noon.

.@BernieSanders-who blew his campaign when he gave Hillary a pass on her e-mail crime, said that I feel wages in America are too high. Lie!

But it didn't end there. Trump renewed his attack on Twitter early Monday, calling Sanders a "wacko" whose "allies [are] coming over to me because I'm lowering taxes, while he will double & triple them, a disaster!"

Strange, but I see wacko Bernie Sanders allies coming over to me because I'm lowering taxes, while he will double & triple them, a disaster!

Sanders on Sunday also sought to make peace, or at least tamp down hostilities, with the Democratic National Committee.

While his campaign has visited some harsh criticism on the DNC, with one unnamed adviser suggesting in a Yahoo! News story on Friday that the party had planted the individual -- since fired -- for improperly accessing Clinton's voter outreach data.

"It's not as if we conjured this guy Josh [Uretsky, Sanders' former national data director] from thin air," the source said. "This is an individual ... who was recommended to us by the DNC and NGP VAN."

Speaking on NBC's "Meet the Press," Sanders only said his campaign was "negotiating" and "trying to work with the DNC to put this whole thing behind us."

Asked if the Democratic party had given him a "fair shot," Sanders again demurred.

"We have had our differences of opinions with the DNC," he said. "But at the end of the day, the DNC, Hillary Clinton and myself -- we want to defeat right-wing extremism in this country."

DNC chairwoman Debbie Wasserman-Schultz, who has taken a lot of grief from Sanders supporters and some unaligned Democrats who believe the establishment apparatus is in Clinton's pocket, appeared moments after Sanders. But the Florida congresswoman was not asked about the data breach or the relationship between the Sanders campaign and Democratic party.